True or False: The terms 9x² and 9xy can be combined.

True or False: The terms 9x² and 9xy can be combined.

• A. True
• B. False
• C. Not sure
• D. Below average

Answer: (B)

To understand the reasoning behind the correct answer, it's important to recognize what constitutes like terms in algebra. Like terms are terms that contain the same variable raised to the same power, but they may have different coefficients. In this specific case, we have the terms 9x² and 9xy. The term 9x² contains the variable x raised to the power of 2, while the term 9xy consists of the variable x raised to the power of 1 and also includes the variable y. Because the variables involved and their respective powers are different in these two terms, they cannot be combined. The first term is specifically about x squared, while the second term represents a product of x and y. Therefore, since 9x² and 9xy do not share the same variable composition in terms of both the variables involved and their powers, they are not like terms. This is why the statement about being able to combine the two terms is false.

To understand the reasoning behind the correct answer, it's important to recognize what constitutes like terms in algebra. Like terms are terms that contain the same variable raised to the same power, but they may have different coefficients.

In this specific case, we have the terms 9x² and 9xy. The term 9x² contains the variable x raised to the power of 2, while the term 9xy consists of the variable x raised to the power of 1 and also includes the variable y. Because the variables involved and their respective powers are different in these two terms, they cannot be combined. The first term is specifically about x squared, while the second term represents a product of x and y.

Therefore, since 9x² and 9xy do not share the same variable composition in terms of both the variables involved and their powers, they are not like terms. This is why the statement about being able to combine the two terms is false.